Dealing a pair in the "hold' em" poker.

ou have been dealt a couple of cards from a well shuffled 52 card deck. What
is the probability that you have a pair?

The index
will identify a pair so that
corresponds to a pair of two's,
corresponds to a pair of 3's, and so fourth... aces correspond to
.
We
have
the n-union below is a total event:
,
hence,
the n-union also consists of disjoint events:
for
,
hence,
we now apply the formula (
Total probability
rule
)
The value of every term above is independent of
.
Moreover,
.
Hence,
because after
there are 51 cards remaining and 3 of them are "two".